IB Maths AA SL 1.1 Number and Algebra Question Bank

Practise modelling arithmetic and geometric sequences, applying finance and logarithm laws, proving results, testing infinite-series convergence and extracting binomial terms.

Syllabus
First assessment 2021
Topic
1.1
Level
SL

Exam points

  • identify sequence parameters before applying nth-term, finite-sum or compound-finance formulae
  • rewrite powers and logarithms with valid laws before solving and checking domain restrictions
  • construct a deductive proof by transforming expressions or linking justified algebraic steps
  • test absolute convergence before applying the infinite geometric-series sum to a context
  • use binomial coefficients and the general term to expand expressions or extract a required coefficient

Covered syllabus points

SL 1.1—Scientific notationSL 1.2—Arithmetic sequences and seriesSL 1.3—Geometric sequences and seriesSL 1.4—Financial applicationsSL 1.5—Integer exponents and logarithmsSL 1.6—Deductive proofSL 1.7—Rational exponents and logarithm lawsSL 1.8—Infinite geometric seriesSL 1.9—Binomial theorem

1.1 Number and algebra - SL content question 1

[Maximum number: 4]

The diameter of a spherical planet is 6×104 km6 \times 10^{4} \mathrm{~km}.

Question (a)

(a)

Write down the radius of the planet.

The volume of the planet can be expressed in the form π(a×10k)km3\pi\left(a \times 10^{k}\right) \mathrm{km}^{3} where 1≤a<101 \leq a<10 and k∈Zk \in \mathbb{Z}.

[ 1 ]

Question (b)

(b)

Find the value of a and the value of k.

[ 3 ]

1.1 Number and algebra - SL content question 2

[Maximum number: 9]

Give your answers to parts (a)(ii), (c)(i) and (d) correct to two decimal places.
Daniela and Sorin have each recently received some money. Daniela won a cash prize and Sorin received an inheritance.
Daniela had two options to choose from to receive her winnings. In both options she receives a payment on the first day of each month for three years.
Option A Each payment is $ 5500.
Option B The first payment is $ 2000. In each month which follows, the payment is 6 % more than the previous month.

Question (a)

(a)

Find the total amount Daniela would receive if she chooses

[ 5 ]

Question (i)

(i)

Option A;

Question (ii)

(ii)

Option B.

Sorin received an inheritance of $ 120000. Sorin invested his inheritance in an account that pays a nominal annual interest rate of 4 % per annum, compounded monthly. The interest is added on the last day of each month.

[ 5 ]

Question (b)

(b)

Write down an expression for the value of Sorin's investment after n years.

Daniela chose Option B and received her first payment on 1st 1^{\text {st }} January 2023. Sorin invested his inheritance on the same day.

[ 1 ]

Question (c)

(c)

Find the value of r if this investment grows to $ 53000 after six years.

[ 3 ]
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